Intersecting two featureclass when one featureclass has overlapping objects!

So I need to run the intersect analysis tool on two feature classes, both are polygons. However, one featureclass contains overlapping objects (buffer regions), and I do not want the output from these intersections. I just want the intersections between the two separate feature classes.

This seems like an issue that there should be an easy fix for, but I can't seem to find a solution...